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Empirical investigation of impact of implementation of FFP.
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DEPARTMENT OF ECONOMICS
Vertical restraints in soccer: Financial Fair Play and the English Premier League
Thomas Peeters & Stefan Szymanski
UNIVERSITY OF ANTWERP Faculty of Applied Economics
Stadscampus
Prinsstraat 13, B.226
BE-2000 Antwerpen
Tel. +32 (0)3 265 40 32
Fax +32 (0)3 265 47 99
http://www.ua.ac.be/tew
FACULTY OF APPLIED ECONOMICS
DEPARTMENT OF ECONOMICS
Vertical restraints in soccer: Financial Fair Play and the English Premier League
Thomas Peeters & Stefan Szymanski
RESEARCH PAPER 2012-028 DECEMBER 2012
University of Antwerp, City Campus, Prinsstraat 13, B-2000 Antwerp, Belgium
Research Administration – room B.226
phone: (32) 3 265 40 32
fax: (32) 3 265 47 99
e-mail: [email protected]
The papers can be also found at our website:
www.ua.ac.be/tew (research > working papers) &
www.repec.org/ (Research papers in economics - REPEC)
D/2012/1169/028
1 Author correspondence: Department of Economics, University of Antwerp, Prinsstraat 13, 2000 Antwerpen,
Belgium. Phone: +32 3 265 41 53, e-mail: [email protected]. 2 Author correspondence: Department of Sport Management, University of Michigan, 3118 Observatory Lodge,
1402 Washington Heights, Ann Arbor, MI 48109-2013. Phone: (734) 647-0950, fax:(734) 647-2808, e-mail:[email protected] Acknowledgements: We would like to thank conference and seminar participants at the University of Maryland, Baltimore County (UMBC), the University of Leuven (KUL), the Lille I-Xiamen-Antwerp micro-economics workshop (Antwerp), the sports and econometrics workshop (Gijon) and the European Conference in Sports Economics (Prague), as well as Jan Bouckaert and Stephen F. Ross for valuable comments and suggestions. We thank Jobin Abraham, Jean-Paul Bewers, Blake Bogdanovich, Jake Kaufman, Tom Lambert, Ben Manko, Karan Mirpuri, Akeeb Patel, Patrick Spicer, Cedrick Song, Robert Snyder, Robert Vanderpluijm, Valeriya Vitkova, and Naglis Vysniauskas for their research assistance. We are grateful to the Flanders Research Foundation (FWO), Cass Business School and the University of Michigan UROP Program for their financial support.
Vertical restraints in soccer: Financial Fair Play and the English Premier League
Thomas Peeters1 University of Antwerp and Flanders Research Foundation
Stefan Szymanski2
University of Michigan
December 2012 Abstract: In 2010 UEFA, the governing body of European soccer, announced a set of financial restraints,
that clubs must observe when seeking to enter its competitions, notably the UEFA Champions League. We
characterize these “Financial Fair Play” (FFP) regulations as a form of vertical restraint and assess their
impact on the intensity of competition in the English Premier League. We build a structural empirical
model to show that introducing FFP would substantially reduce competition, resulting in lower average
payrolls, while average revenues would hardly be affected. Depending on the exact regime, wage to
turnover ratios would decline by 8% to 15%.
Keywords: vertical restraints, soccer, Financial Fair Play
JEL-codes: L42, L83, L51
2
1 Introduction
Vertical agreements are usually defined as concerted practices among undertakings operating at
different levels of a production or distribution chain (see e.g. Zanarone (2009) p691). Typical examples
include restraints placed on car dealerships by manufacturers, on bars and pubs by brewers or on high
street retailers by producers of luxury goods. In this paper we analyze a more unusual type of vertical
restraint, one placed by a governing body on professional sports clubs aiming to compete in its
championships.
The governing body in question is UEFA, which holds jurisdiction over soccer played in Europe, and
organizes the UEFA Champions League. This international club competition generates over €1 billion a
year from broadcasting contracts negotiated by UEFA, and a large part of this revenue is paid out to
participating soccer clubs as prize money. It is therefore a vital source of income to most of the
participating clubs. Since 2004/05 UEFA has introduced the “club licensing” system which sets out
minimum standards relating to stadium quality, administration and legal documentation. Clearly, club
licensing functions as a set of vertical restraints, much in the same way that for example car
manufacturers try to preserve quality standards at their dealerships. Recently UEFA added requirements
relating to solvency and financing to the club licensing system. These regulations, which are commonly
referred to as “Financial Fair Play” (FFP), are the main focus of this paper.
FFP has essentially two dimensions, one which requires soccer clubs entering UEFA competition to
be solvent and the other which requires them to limit their spending on players to the extent of their
“football income” 3: the so-called break-even rule. UEFA justifies these rules on efficiency grounds: “to
improve the economic and financial capability of the clubs” and “to protect the long-term viability and
3 Soccer is referred to as football in Europe, and as such UEFA uses football instead of soccer in its phrasing of the
FFP rules.
3
sustainability of European club football.” However, these regulations might just as easily be seen as a
means of restricting competition in the Champions League itself or in the national league championships.
In particular, the break-even constraint may limit club expenditure on player wages and as such increase
the profitability of clubs. This would allow UEFA to retain a larger share of broadcast revenue, thus
enabling both the clubs and UEFA to extract rents at the expense of the players.
In this paper we examine to what extent the FFP break-even rule would restrict competition in the
English Premier League (EPL). We develop a model of competition at the club level with two crucial
ingredients, a contest success function linking match outcomes to payrolls and a revenue function linking
financial gains to on-pitch performance. We estimate the model combining accounting with sporting
performance data. We then use simulations to show that, depending on the exact regime, the
enforcement of FFP could reduce labor costs in the English Premier League by as much as 22% without
significantly impacting on revenues. In other words, competing clubs succeed in restricting horizontal
competition using a vertical agreement.
The paper is set out as follows. In the next section we discuss the outline of our analysis in the
context of the relevant literature. Section 3 describes the structural model and section 4 describes the
data and estimation procedure. Section 5 presents the estimation results and section 6 the simulation
results. The final section discusses our conclusions.
2 Sports league competition and vertical restraints
There is a substantial literature on vertical restraints, both from a theoretical and empirical point
of view. In theory restraints may be pro-competitive, enhancing the capacity of independent businesses
to co-ordinate in the efficient delivery of goods and services, which might otherwise be plagued with
externality problems such as double marginalization, hold-up and free-rider problems (see e.g.
4
Mathewson and Winter (1984) and Rey and Tirole (1986)). Lafontaine and Slade (2008) review the
empirical evidence on the economic impact of vertical restraints and find that different studies often
produce contradictory results. There appears to be a general tendency for restraints imposed by
manufacturers on retailers to have pro-competitive effects, largely because the manufacturer usually has
an incentive to make sure that consumers receive the product in the best possible condition. In any case,
many puzzles remain about the competitive effects of vertical restraints and generalizations are
problematic. In this paper we construct a structural empirical model of a specific industry, professional
soccer in England, and assess the impact of a vertical restraint by simulating the counter-factual
equilibrium. In that sense we follow the papers by Asker (2005), Brenkers and Verboven (2006) and
Ferrari and Verboven (2012), which have taken this approach to examine restraints in the beer, car and
magazine industries, respectively. We provide evidence of the anti-competitive impact of this restraint,
which at first glance seems to operate as a quality standard, rather than a coordination device.
Considered as economic entities, professional team sports leagues are unique in the degree of
co-ordination that is permitted among ostensibly competing businesses. In North America and Europe
sporting competitors are allowed to agree the rules of the game and to collectively manage activities
such as the sale of league broadcasting rights. On the one hand it is clear that the sporting competition
itself cannot exist without “collusion” over the setting of the sporting rules. On the other, the rationale
for allowing competing sports organizations to agree on economic issues is less obvious. The courts in
both Europe and the US have sought to draw a distinction between “sporting rules” required for the
regulation of an orderly and attractive contest, as opposed to rules that are intended to restrict
competition and benefit the contestants. Thus for example, the European Commission in its White Paper
on Sport (2007) recognized the “specificity of sport” while affirming that “Competition law and Internal
Market provisions apply to sport in so far as it constitutes an economic activity”.
5
Horizontal restraints are commonplace and have been extensively analyzed (and litigated) in the
context of North American sports leagues. For example, salary caps have existed for some time in
American leagues; the first was introduced in the National Basketball Association in 1984 and the
National Football League adopted a salary cap in 1994.4 The caps were the result of a collective
bargaining agreement between union and team owners, with a view to fixing the percentage of league
revenues that would accrue to the players. The effect of a salary cap on player earnings, league
performance (competitive balance) and total welfare has been extensively discussed in the literature;
see e.g. Fort and Quirk (1995), Vrooman (1995), Késenne (2000b) and Dietl et al. (2009). Since the
American-style cap is intended to place a common limit on all teams (usually defined as a fixed
percentage of league revenues), it is generally thought that its main effect is to reduce the variance of
team performance (equalizing results), although Vrooman (1995) argues that the main purpose of the
cap is to hold down salaries while teams evade the effects of the cap by working around the constraint.
A fundamental difference between the American and European sports leagues system concerns
the role of governing bodies. Governing bodies generally exist to promote the development of sport
inside a particular country, and to manage the preparation and participation of national teams in
international competition (e.g. the Olympics or the FIFA World Cup). In the US the jurisdiction of
governing bodies is limited by law to the administration of amateur sports, and the professional leagues
are self-governing.5 In Europe (and most of the world) governing bodies claim jurisdiction over both
amateur and professional sport. National soccer associations in Europe were mostly established before
the First World War (the English Football Association (FA) being the first, created in 1863), and
professional or semi-professional domestic leagues were created contemporaneously. UEFA, by contrast,
4 We describe these as horizontal restraints because the NBA and NFL represent nothing more than the collective
will of the owners, by contrast with governing bodies in soccer, discussed below. 5 The situation in the US is presently regulated by the Ted Stevens Olympic and Amateur Sports Act (36 U.S.C. Sec.
220501)
6
was created in 1954 with limited powers. Interestingly, the European Champion Clubs’ Cup (which
eventually evolved into the Champions League) was initiated in early 1955, not by UEFA, but by Gabriel
Hanot, a soccer journalist working for the French sporting newspaper L’Equipe. Only later that year, just
before the competition began, was UEFA persuaded to take over its administration (Murray (1994),
pp166-7).
UEFA’s role in European soccer has expanded dramatically since its foundation, and it is involved
in many aspects of the development of the game as well as running a variety of competitions. However,
its financial position and prestige rests almost entirely on its control of the Champions League. According
to its 2010/11 Financial Report UEFA generated €1385 million from the sale of broadcast and commercial
rights to its competitions and paid out €1001 million to participating clubs, leaving around 28% of
revenues to cover its own costs and discretionary spending. Until the introduction of the club licensing
system in 2004, UEFA imposed few restrictions on clubs. The purpose of club licensing was to impose a
minimum set of standards, thus having the character of a set of vertical restraints. The original
investigation into the creation of a licensing system in 1999 also considered the imposition of a salary
cap which was at the time considered infeasible. The 1995 Bosman judgment of the European Court of
Justice had demonstrated that regulation which restricted competition in the market for players that was
not backed by pro-competitive reasoning was doomed to failure under EU law.6
In 2010 UEFA announced the introduction of the Financial Fair Play (FFP) regulations into the
club licensing system. These rules can be divided into two parts. The first deals with insolvency, a chronic
problem which has plagued European soccer clubs; this issue is examined in a related paper (Szymanski
(2012)). The second part deals with the break-even rule, the focus of our paper, which requires that
6 The relevant European law in the Bosman case concerned the freedom of movement of labour, but UEFA also
became embroiled with the European Commission over the collective sale of broadcast rights, a competition law issue.
7
“relevant expenses” must not exceed “relevant income”. The definition of “relevant” is highly specific,
and on the revenue side covers mainly income from broadcasting, match-day income (e.g. ticket sales)
and sponsorship. It excludes, for example, direct subsidies from wealthy owners.
We will argue that the break-even rule operates analogously to a salary cap. As mentioned
above, the key benefit that is claimed for a salary cap in North America is that it promotes competitive
balance amongst the teams in the league. Clearly, since FFP only limits spending of an individual club in
proportion to its own resources, and these resources vary hugely in European soccer, no such benefit
can be claimed. Indeed, some have argued that the break-even rule will reduce competitive balance by
limiting the opportunity of smaller teams to erode the dominance of the established teams since they
will not be able to use outside resources to fund a challenge. Proponents of the break-even rule claim
that this is indeed a benefit to the clubs, since the only sources of outside resources are debt, which adds
risk to the system, and equity injections from “sugar daddies”, which undermine the integrity of
competition by turning soccer into a wealth contest rather than a sporting contest.
This paper shows how the impact of the restraint goes beyond those clubs wanting to spend
more than their soccer resources. Given that higher spending tends to generate better sport
performance, restraining the spending of some clubs reduces the cost of winning for all clubs. Thus there
will be spill-over effects to clubs not directly affected by the limit, by lowering the cost of achieving a
given level of success. The simulation results from our structural model show that the effect on total
payroll spending is substantial. Once fully operational, the FFP rules could reduce the ratio of payroll
spending to turnover by up to 15%. Essentially, the vertical restraint introduced by UEFA would result in
a comparably anti-competitive outcome, as the horizontal agreements between competing firms, which
exist in the US under the form of salary caps.
8
This result has already been discussed in a theoretical context by Dietl et al. (2009) who examine
the effect of a salary cap based on a fixed percentage of team income, exactly the kind of cap imposed
by the FFP break-even rule. Their model shows that while implying more variation in spending than an
American style cap, it unequivocally reduces aggregate salaries.
Ours is not the first paper to consider FFP. Two recent papers by Madden (2012) and Franck and
Lang (2012) build theoretical models to analyze the effects of FFP on so-called “sugar daddy” owners,
who bail out their club in case of financial losses. Both papers reach different conclusions, as Madden
(2012) finds negative welfare effects from FFP, while Franck and Lang (2012) identify conditions under
which FFP enhances welfare. Muller et al. (2012) analyze the FFP rules from a largely ethical standpoint.
They claim that allowing team owners to inject their own funds into a club amounts to “behavior that
damages the integrity of the competition or violates sport-ethical standards” and advance this as a
justification for restrictions under FFP. Finally, Szymanski (2012) examines FFP from the point of view of
controlling insolvency problems, examining the causes of 67 known cases of insolvency in English
professional soccer.
From a modeling perspective, sports leagues should be viewed as a kind of rent-seeking contest
where success in sporting competition depends on the relative share of total resources devoted to
competition (e.g. Tullock (1980)). There is an extensive theoretical literature on rent seeking contests
(much of which is reviewed in Konrad (2009)). Szymanski (2003) argued that sporting competitions in
general should be viewed as rent seeking contests since they exhibit a “fixed supply of winning”. Each
season consists of a fixed number of games, and the winning team is the one that gains the largest
possible share of wins, teams expend resources in the form of effort or money to gain the largest
9
possible share. 7 The literature on professional sports leagues, starting from Rottenberg (1956),
recognized the existence of the fixed supply but did not adapt the contest literature results to the
modeling of league choices (see e.g. Fort and Quirk (1995), Vrooman (1995)). This literature assumed
that teams could choose the level of success they achieved, independently of the choices of the other
teams, which cannot be true in a proper contest setting (see Szymanski and Késenne (2004)).
Empirical models of American sports leagues starting with Scully (1974) assumed that teams
invested in talent to the point where the marginal revenue product (MRP) equaled the wage, where MRP
was the product of the player’s marginal contribution to winning multiplied by the marginal revenue to
the team of a win. This approach was then used to show the discrepancy between wages and MRP when
team owners possessed monopsony power, and the erosion of that monopsony power in the era of
collective bargaining and limited free agency (see e.g. Kahn (2000)). The fixed supply of winning is
accounted for neither in these models nor in the empirical models of European leagues (e.g. Szymanski
and Smith (1997), Garcia-del-Barrio and Szymanski (2009)). Likewise, there is a substantial literature that
seeks to estimate a production function for wins (relating resources to success) in order to identify the
relative efficiency of teams in a league (e.g. Barros and Leach (2006), Lee and Berri (2008)) and these too
ignore the problem of modeling the fixed supply.
In this paper we explicitly model the contest among clubs using a Tullock contest success
function which we can estimate using game-by-game results and accounting data on resources devoted
to winning in the form of team wage expenditure. While there is an extensive theoretical literature, the
literature on the estimation of contest success functions is sparse (see e.g. Jia et al. (2012)).
7 In league soccer the success of a team is generally recorded in the form of points scored, and until the 1980s a
drawn game was treated as equivalent to half a win. Since then leagues have adopted a system of awarding three points for a win and one for draw. One implication of this is that the total number of points awarded in a season depends on the number of draws. However, the league still remains essentially a zero sum game.
10
3 Model
To simulate the introduction of Financial Fair Play we need to model the best response of the clubs
to the policy shift. In our model teams try to win by devoting resources, because the outcome of
competition depends on the relative share of invested resources. Revenues and profits are then
determined by contest success. As will become clear, FFP will affect the equilibrium by altering the
budget constraint of the teams. We now discuss the model setup in more detail.
3.1 Model Setup
(a) The sporting competition and the contest success function
A typical European soccer league consists of clubs divided into hierarchical divisions (or tiers),
where mobility between divisions is permitted by the system of promotion and relegation. 8 Each division
in year contains teams that play each other twice in season, once at home and once away,
generating contests for each club in a season. In each contest the probability of success
depends on the playing resources of the team which we label . At the match level a contest success
function (CSF) relates the payrolls of the home and away team to the probability of winning, drawing or
losing the game. 9 We adapt the standard Tullock CSF to allow for the possibility of a draw. We use the
following specification10, where denotes the result of a game between team i and j at the home
stadium of team in season t:
8 Under this system teams finishing at the bottom of the league table are forced to play in a lower division in the
following season (relegation), whereas teams finishing at the top of the table gain the right to play in a higher division (promotion). In other words, sporting merit determines which teams play in the higher tiers, as opposed to the league choosing which cities may host teams, as is common in the American major leagues. 9 Draws are common in soccer, with about 30% of games ending in a tie. In contrast to most other team sports,
there is no tie-breaking mechanism during the regular season, instead each team is awarded 1 point in the league table. 10
An alternative specification to allow for draws in the Tullock CSF has been proposed by Pavlo Blavatskyy (2010). In his specification however, the probability of a draw necessarily declines in the sum of both investments, which is a clearly not a feature of soccer contests. Hence, we choose to introduce this alternative.
11
(1a)
(1b)
(1c)
Where
represents the advantage derived from being the home team. This may stem from a number
of factors such as the bias of the fans toward the home team, the convenience for the players
(e.g. less travel) or the bias of the referees (see e.g. Garicano et al, 2005).
is the productivity of team i in transferring resources into win probability, for example
this may reflect the relative effectiveness of the team manager or “team spirit”.
is the Tullock parameter, which captures the sensitivity of the contest to the relative
investments of each team. We allow this sensitivity to vary by league division.
is a season-division specific constant which measures the baseline probability of a draw, i.e.
when both teams would be equally matched in the contest.
is a parameter measuring the sensitivity of draws to the variance of team resources. We
expect that contests where both sides are more heterogeneous have less probability of ending a
draw.
To measure we will use club payrolls for which accounting data is available.11 Previous research
has shown that payrolls in soccer are highly correlated with team success over the season (see e.g.
Szymanski and Smith (1997), Forrest and Simmons (2002)). Playing talent is highly mobile and the typical
11
The accounting data refers to total payment to all employees, but almost the entire wage bill is paid to the players.
12
means of attracting a player is to offer a significant increase on their current wage. The issue of reverse
causality (the possibility that success leads to higher wage payments) does not arise since seasonal wage
payments will not be significantly influenced by the outcome of individual games (teams play between
38 and 46 league games in season). Thus in our model we can measure “effective effort”12 as talent
resources (wage payments), the effectiveness with which those resources are used and the context
(home or away). The outcome of the contest then depends on these inputs and the sensitivity of winning
to relative resources.
In European soccer leagues, a win is awarded three points and a draw one point. Given that each
team faces every other team once at home and once away, we may therefore calculate the expected
end-of-season points total as:
(2)
Since the number of points a club can obtain varies in a given season, we rescale by the total number
of points obtainable in season t, i.e. , and denote this relative points total as .
(b) Revenue and Profit
Each season , every owner sets a budget constraint which is either a positive amount the owner
wants to earn, or a negative amount which the owner is willing to put into the club. Thus teams can be
thought of as win maximizers subject to budget constraint rather than profit maximizers. Almost all
researchers since Sloane (1971) have emphasized the lack of profit orientation in European soccer, and
win maximization is the most commonly assumed objective, see e.g. Késenne (2000b).13 Andreff (2007)
and Storm and Nielsen (2012) emphasize that within this framework the soft-budget constraint facing
12
We will continue to use this term to refer to and
. 13
Also note that win maximization leads to the most generous estimate of the counterfactual payrolls, which underlines the significance of our results.
13
many of the teams can be negative, which we model by assuming that may take a negative value.
Given the constraint set by the owner, club managers attempt to win as many points as possible setting a
payroll . The manager behaves as a cost minimizer towards non-payroll costs, , which include
overhead costs such as maintenance of the stadium. We assume these costs are independent of the
payroll decision.
Club revenues, , are modeled as a Cobb-Douglas function of the club’s capital stock,14 , relative
points obtained, , time-varying league-wide factors,15 , and constant club-specific unobservables,16
. This gives us,
(3)
Combining the elements (1a)-(3) allows to formulate the profit function for club i in reduced form as
from this, the manager’s optimization problem is to solve
, subject to . As we expect a positive impact
of payroll on win probabilities ( ) for all values of , optimizing the number of points boils down
to setting the highest payroll allowed by the revenue generating capacity of the club and the budget
constraint. The best response in terms of payroll, , may therefore be found as the implicit solution of
the budget constraint when it binds:
(4)
Note that (4) only generates a pure strategy Nash-equilibrium for certain ranges of the parameter values.
In particular, if winning and revenues are too sensitive to payroll and relative points, respectively, then
there will only be an equilibrium in mixed strategies (see e.g. Baye et al (1994)).
14
By far the most valuable asset teams own is their stadium. As such, this capital stock variable may be interpreted as the value of the stadium, which is proportional to its size and quality. 15
E.g. the value of the league-wide media rights deal 16
E.g. the size of the club’s support in the local market, commonly referred to as drawing power in the literature.
14
3.2 Introducing Financial Fair Play
In our policy experiment we focus on the break-even requirement in the FFP regulations. This
requirement stipulates that a club’s “football-related costs” should not be greater than its “football-
related income”.17 In terms of our model, we interpret this as UEFA setting a lower bound, , on ,
the (negative) amount the owner gets out of the club, or conversely, an upper bound on the amount he
may put up to finance the club’s losses.
FFP has a direct effect on clubs for which this new constraint is binding, i.e. when . The
budget constraint for affected teams becomes
(5)
where denotes the updated best response payroll. As we have assumed other costs, , are
minimized and independent of the payroll decision, the manager has to set a lower payroll under FFP.
The direct effect of the break-even requirement is therefore a decline in payrolls for affected teams.
However, when payrolls across the league are lower, all teams will, ceteris paribus, win more points and
revenues for a given payroll. Note that even a club whose budget is constrained by FFP will benefit from
this effect if there are other clubs also constrained by FFP.18 Following our assumption that clubs are win
maximizers, we also assume that the response of clubs is to spend this extra revenue (slack) up to the
point where their budget constraint binds again (whether that constraint is directly affected or
unaffected by FFP).19 This indirect effect of FFP therefore leads to higher wage bills for teams not
17
More details can be found in articles 58-63 of the FFP regulations (UEFA, 2010). 18
Imagine, for example, that there are two clubs that are bound by FFP, one by £1 million and the other by £100 million. The first club will reduce expenditure due to the direct effect, but will almost certainly increase expenditure by more because of the indirect benefit of the other club’s reduction in expenditure. 19
Alternatively, we could assume the owner pockets the additional revenue, i.e. wage bills for the unaffected teams are constant. This would only reinforce our conclusion that the wage to turnover ratio decreases, while the distribution of points be more stable.
15
constrained by FFP, and possibly even for some teams constrained by FFP. There are three possible
cases:
(i) If for all i (FFP does not bind any clubs) then FFP does not affect payroll
(ii) If for only one club, then payroll falls for that club and increases at all other clubs
(iii) If for more than one club, then (a) payroll falls for at least one club bound by FFP
and (b) payroll rises at all clubs not bound by FFP.
Thus in case (iii) there can exist clubs who are bound by the FFP constraint but still increase their payroll
due to the indirect effect of the FFP constraint binding on other clubs.
4 Data and estimation procedure
In order to estimate the model we need to identify all elements of the equilibrium condition (4). The
financial information is taken from the audited financial accounts of teams in the top 3 tiers of English
soccer over the 1993/94-2009/10 seasons. Under English law limited companies (all English soccer clubs
are owned by limited companies) are obliged to file their annual report and accounts at Companies
House, which are then accessible to public for a small fee.20 We assume that the budget constraint set by
the owner, , can be proxied by the financial profit or loss reported by the club in a given year. We can
also back out the magnitude of non-payroll costs, , as the difference between turnover minus wage
costs and the profit/loss for the year, which we all observe in the accounts.
We estimate the CSF given by equations (1a) - (1c) using a maximum likelihood procedure. As (1a)-
(1c) directly describe a probability for each outcome, we simply minimize the difference between these
probabilities and the actual outcomes in the data. The main problem we face when estimating the CSF, is
that we cannot directly observe firm productivity, . As more productive clubs can afford to invest
20
http://www.companieshouse.gov.uk/.
16
more in payroll, because their marginal return of winning on wage spending is larger, payroll and
productivity are expected to be positively correlated. Running the estimation without controls for
would therefore lead us to overestimate .
This problem has been discussed extensively in the production function literature (see Olley & Pakes
(1996) and Levinsohn & Petrin (2003) for two seminal papers on this issue), where it leads to upward
bias of the labor coefficient. We correct for this upward bias in a couple of different ways. First, we
introduce fixed effects (FE) for each club in the estimation procedure. We implement this by including a
dummy for each team, which is equivalent to assuming that productivity is constant over the sample
period, . This is clearly a very limiting assumption. We relax this assumption in a second
approach by introducing time-varying firm specific effects. We split up the sample period in different
ways, and report both the results with three and four sub-periods. 21
In the production function literature, using (time-variant) firm specific effects has usually been
avoided, as it leads to unrealistically low estimates of the coefficients on fixed inputs (i.e. capital). As an
alternative we follow Levinsohn & Petrin (2003), who suggest including a polynomial of observables
which are correlated with productivity into the estimation. This polynomial functions as a proxy for
productivity, taking away the upward bias, while still being more flexible than fixed effects. In our
application the tenure of the current team manager serves as an instrument for on-field productivity. We
conjecture that a positive correlation between tenure and productivity exists, because teams usually fire
their manager in response to on-field performances which fail to live up to expectations. As such, a
longer tenure for the current manager is only possible if the team manager has been productive enough
to avoid being dismissed.
21
The 3 sub-periods reported here are 1994-1998, 1999-2004 and 2005-2010, the 4 sub-periods are 1994-1997, 1998-2001, 2002-2005 and 2006-2010.
17
We also add the level of tangible fixed assets in the club to the polynomial. The intuitive argument
here is that more productive teams, who obtain wins more cheaply, also have a stronger incentive to
build the revenue generating capacity of the team, i.e. its capital stock. We use both of these
instruments by including a fourth order polynomial of logged manager tenure measured in games and
logged tangible fixed assets. A final issue in obtaining the estimates, controlling for firm productivity, is
that given the CSF structure, productivity may only be interpreted relative to competitors. We therefore
define one team-season to serve as the reference team, for which we restrict .
Table 1 shows summary statistics for the CSF dataset. We assemble an initial data set of 25,392
observations22 at the game level from http://footballresultsonline.co.uk. We then drop all observations
where the accounting year for the club did not correspond to the soccer season or wage data are missing
from the accounts.23 Thus we obtain a match level data set of 20,324 observations. Our dependent
variable is the home team’s result (res), where 0 signifies a loss for the home team, 1 a draw and 2 a
home win. About 45.8% of all games were won by the home team, while a further 27.5% ended in a
draw, which indicates the significance of home advantage. The payroll variable includes wages plus
relevant social security payments and taxes, as it is meant to signify relevant employment costs, rather
than net wage. Although payroll inflation has been dramatic (averaging over 10% per year across the
sample period), we do not need to control for this in estimating the CSF since the outcome depends only
on the share of payroll resources in a given season. The summary statistics in Table 1 reveal the huge
financial disparities in English soccer. For example, the maximum spent on wages by an individual team
amounts to more than ten times the average payroll of £16m over the sample period.
<insert table 1 around here>
22
We excluded play-off games which determine promotion to higher tiers, as these do not generate points for the final ranking. 23
Usually wage data are missing either because clubs filed abbreviated accounts or because they failed to file accounts in case of insolvency proceedings. For the 1160 club seasons in the sample period we have 90% of the audited wage bills.
18
The season-division data show that the sample contains most games from the second tier with
40.7%, whereas the third tier makes up only 28.6% of the data. This is because (a) for most of the period
there were fewer teams in the top tier and (b) several teams at the lower levels file abbreviated accounts
without wage information. Finally, the table shows summary statistics for the variables included in the
productivity polynomial. These are the tenure of the current manager, measured as the number of
consecutive games the team played under his supervision and the stock of tangible fixed assets in the
club.
<insert table 2 around here>
A final element of the model we need to identify is the revenue equation (3). We use data on
revenues24 and assets from the financial accounts matched with sports data from the RSSSF archive25 to
estimate this equation at the club-season level. Again dropping observations for which revenue data are
missing or the accounting year does not correspond to the season, gives us an unbalanced panel of 87
clubs over 17 years. Table 2 displays summary statistics for the data set, where all financial variables are
expressed in millions of 2010 UK Pounds. Revenues and capital stocks (tangible fixed assets) vary quite
dramatically. Most of this variation plays between leagues and seasons, rather than between clubs in the
same league-season. In about 10 percent of all observations the club is part of a larger legal entity. In
that case, a part of the tangible fixed assets are often transferred to the holding company, which leads us
to underestimate the true capital stock. We therefore include a dummy not ultimate parent, when an
observation suffers from this issue. We also control for promotion or relegation of the club, which is
especially relevant given the considerable “parachute payments” teams receive upon relegation from
24
As FFP looks at “football related revenues”, we have taken out revenues which were explicitly labeled non-football in the accounts. There were only three such cases, Arsenal (property development), Bolton Wanderers (hotel) and Sheffield United (conferences). 25
www.rsssf.com.
19
the Premier League.26 Finally, the division and season dummies indicate that our observations are
homogeneously spread across divisions and seasons.
<insert figure 1 around here>
Figure 1 shows the key financial variables in the dataset split out by division. In the upper-left
panel we clearly see a huge increase in revenues over the last decade, especially in the top division. The
upper-right panel however shows that average wage bills have followed a similar upward trend. The
overall wage-to-turnover ratio, a key indicator of profitability in sports leagues, has therefore gone up in
all three divisions. As can be seen in the bottom-left panel, this has meant average profits have
plummeted.
5 Estimation Results
Table 3 shows the estimation results for the CSF (Tullock) parameters. Overall, the estimates confirm
that the model is well behaved, as all parameters have the expected signs. The return parameters,
through , are positive and significant, so wage spending translates in higher win probabilities.
Judging from the estimates, returns to investment appear to be highest in the Premier League. One
explanation for this may be that the distribution of talent is more skewed at the top end of the talent
distribution, so that a given ratio of wage payments generates a higher probability of winning at the
highest level.
The home advantage parameter, , is significantly larger than 1, confirming that home advantage
matters in English soccer. The significance of the draw parameter shows that draws are more likely
when opponents are more closely matched in terms of their effective efforts. For simplicity table 3 does
26
In the EPL a part of the media rights revenues is given to the teams relegated in previous seasons. In 2010 these “parachute payments” amounted to more than £15m, see http://www.premierleague.com/engb/news/news/broadcast-payments-to-premier-league-clubs.html for more on the EPL distribution scheme. There is no compensation for clubs relegated from the second to the third tier.
20
not report all the season-division dummies, , included in the draw probability. Instead we report the
average and standard deviation of . The estimate implies that a match between two equal opponents
in terms of effective efforts has about 30% chance to end up in a draw. This number is fairly stable across
different estimation approaches, seasons and divisions.
<insert table 3 around here>
In terms of correcting the upward bias in the return parameter, the various approaches we
employ lead to similar results. When we control for unobserved productivity differences, the estimated
return on investment in the first division is significantly lower. The estimated return parameter in the
other divisions turns out to be slightly higher, although the difference is often insignificant. The other
parameters in the estimation remain unchanged by adding controls, which is in line with our
expectations.
<insert table 4 around here>
To understand why controlling for productivity has different effects on the estimated return
parameters across tiers, we need to examine the pattern of estimated firm productivities given in tables
4 and 5. These productivity estimates are obtained by calculating the firm specific effects and polynomial
values for all teams. Since these may only be interpreted relative to competitors, we scale each
estimated by the average over the tier and season. A first thing to note from table 4 is that the
implied productivity measures from all approaches are highly correlated, which confirms that there is
consistency over different approaches. Interestingly, the correlation between payroll and productivity is
both positive and large, but only in the top division. We suspect this is the result of promotion and
relegation. In the lower tiers newly relegated teams are often able to keep high payrolls,27 while not
27
This may be due to parachute payments and/or to the fans sticking with their club when it is relegated, at least in the short run.
21
being more productive than the league average. This effect counteracts the fact that productive teams
generate wins more cheaply and may therefore invest more.
Table 5 shows the average, standard deviation and average maximum-to-minimum ratio of
productivity split out by division. The table shows that introducing varying firm specific effects leads to
larger varieties in the estimated productivities. Also, the standard deviation and maximum-to-minimum
proportion in the top tier turn out to be significantly larger across all productivity measures, which
means that the productivity gap between teams is greater there. This result is intuitive, because we
would expect the system of promotion and relegation to lead to a clustering of highly productive teams
at the very top of the tier system. The combined effect of the poor link between payroll and productivity,
and the smaller productivity gap explains why we do not find the return coefficient to decrease when
controlling for productivity. However, when the link between wages and productivity is absent and
productivity differences are low, there is no reason to expect an upward bias in the return parameter in
the first place.
<insert table 5 around here>
Estimation results for the final element of the model, the revenue function, are depicted in table
6. We report pooled OLS, random and fixed firm effects estimates. Across all estimation methods, every
significant coefficient has the expected sign. Introducing firm specific random or fixed effects decreases
the size of the estimated coefficients. Given that most firm specific dummies turn out to be significant,
we reject using the simple pooled OLS estimates. A Hausman test shows that there is no consistency
between the random and fixed effects estimates, so we restrict our attention to the fixed effects results.
Since we have assumed a Cobb-Douglas specification, the points and assets coefficient should be
interpreted as an elasticity. This means that a 1% increase in relative points relates to about a 0.39%
increase in revenues and a 1% increase in the value of tangible assets leads to a 0.08% increase in
22
revenues. To give an indication of the economic relevance of the estimate of the points parameter, we
calculated the monetary value of an additional point in the EPL 2010 season for each team. We find the
average value to be £683k, with a minimum of £305k and maximum of £1405k.28 The results show that
relegated teams indeed hold a revenue advantage, which can largely be attributed to the “parachute
payments” which the Premier League pays to relegated teams, whereas promoted teams do not seem to
be at a disadvantage compared to their division competitors. This result confirms our hypotheses that
newly relegated teams are able to sustain higher payrolls in the short run, while not necessarily being
very productive.
Our control variable for not being the ultimate parent company is significant and positive. This
compensates for the possible underestimation of the capital stocks for these clubs. We also estimated
the model dropping all observations for which the club is not the ultimate legal parent entity, which led
to very similar results. We do not report every individual season-division dummy to enhance the
readability of the table. The pattern in these dummies corresponds to our expectations, i.e. they are
increasing towards higher tiers and later seasons. In terms of the overall fit of the model, we achieve R-
squared statistics which are consistently around 0.9, a reassuring number.
<insert table 6 around here>
6 Simulation Results
We now use our estimates to simulate the impact of the break-even condition of the Financial Fair
Play regulations. Strictly speaking the regulations apply only to teams that qualify for participation in
UEFA competition, which consists of only the top teams in the Premier League. Rather than focus on this
arbitrary group (whose identity fluctuates significantly from year to year), we simulate the effect of
applying FFP to all clubs in the Premier League. UEFA would certainly like to FFP adopted more broadly,
28
These values are for Wigan and Manchester United, respectively.
23
and in the summer of 2012 the second tier of English soccer (the Football League Championship)
announced that it would adopt comparable regulations. For our simulation we consider the most recent
season for which we have data, which is 2009/10.
A first issue in doing the simulation is the bankruptcy of Portsmouth FC during the 2010 season,
which caused the club not to file accounts for the financial years ending 2009 and 2010. We use
Portsmouth’s 2008 figures as a proxy for the missing values of wages and assets. We assume that these
figures do not change when calculating counterfactual scenarios, but drop the team’s figures from all
calculations of the effects of FFP and the assessment of the model.
<insert table 7 around here>
In a first step we predict the end-of-season points using the actual 2010 EPL payrolls. Table 7
shows summary statistics and standard goodness-of-fit measures for the end-of-season points using
different estimation approaches. As a reference, we also report these measures for a null-model where
the probability of each match outcome is equal to its frequency in the dataset. All the simulation models
exhibit a slightly lower average point total than the actual results. This is due to the exclusion of
Portsmouth, which has a larger points total in our simulation than in the real rankings. The standard
deviation in the simulated models is slightly lower too, especially when productivity is not (or poorly)
controlled for.
The root mean squared error (RMSE) and the mean absolute error (MAE)29 clearly support the
validity of the CSF model. Even in the simple model without productivity controls, the prediction error
goes down by more than 50%. Among the different estimation approaches the varying-firm-effects
29
The root mean squared error is calculated as the square root of the average of the squared difference between
the predicted and actual values, i.e. . The mean absolute error is given by
.The advantage of these measures compared to the mean squared error is that they are measured in
the same units as the basic problem, making them easier to interpret.
24
models appear to result in the best fit for the 2010 season. In both models the average error declines by
almost 10 points compared to the null model, whereas the RMSE reduces to about a third of its value in
the null model.
When simulating the introduction of the break-even constraint, we try to keep as close as
possible to the actual FFP regulations. These stipulate that the “difference between relevant income and
relevant expenses is the breakeven result” (UEFA, 2010, p.34) and the accumulated breakeven result
over the three previous seasons should not amount to a loss greater than the “acceptable deviation”. For
the 2013/14 and 2014/15 seasons this deviation is set to €45m, or an average of €15m per season, for
the 2015/16, 2016/17 and 2017/18 seasons to €30m or €10m per season. After this phasing in period,
the accepted deviation would eventually come down to €5m over three seasons, although UEFA has not
yet determined a time scheme for this to happen.
We look at four scenarios, which correspond to an average accepted deviation of €15m, €10m
and €5m per season, and the “final” scenario with a total acceptable deviation of €5m over three
seasons.30 We implement this policy change by looking at each team’s combined losses for the 2007/08,
2008/09 and 2009/10 seasons. If these losses exceed the acceptable deviation, we diminish the club’s
payroll for the 2010 season by the amount necessary to comply with the breakeven constraint. Given
these new payrolls, we recalculate the end-of-season points and revenues using our estimation results
for equations (1a)-(3). We then re-evaluate whether the affected teams comply with the breakeven
constraint and diminish their payroll further if necessary.
Our assumption of win maximization, implies that clubs which generate extra revenues as a
consequence of FFP do not pocket these extra resources. We therefore add any revenue increase over
30
In accordance with the FFP rules we convert these amounts to UK Pounds using the average ECB exchange rate over the reporting period, retrieved from: http://sdw.ecb.europa.eu/browseTable.do?node=2018794&CURRENCY=GBP&sfl1=4&DATASET=0&sfl3=4&SERIES_KEY=120.EXR.D.GBP.EUR.SP00.A
25
the original predicted revenue to the existing payrolls. Using this new set of payrolls we again calculate
the end-of-season points and revenues using equations (1a)-(3). We iterate these steps until we reach a
fixed point, which satisfies the breakeven constraints under FFP (5). We obtain standard errors on this
simulation using a bootstrap procedure. We repeat the simulation 200 times using a set of independent
draws from the distributions of the parameter estimates for each iteration. We then establish the
sample standard error on all variables of interest and report these in the table.
<insert table 9 around here>
In table 8, we depict the change in payroll together with the original payroll levels for each team.
The asterisks indicate whether a team is facing a payroll restriction because of FFP, which reveals that
more than half of EPL teams would be affected. All unaffected teams put up higher wages, because they
re-invest the extra revenue they generate under FFP. In most cases the restricted teams end up with a
net decline in payroll, i.e. the direct effect of FFP dominates. In a couple of cases however, a restricted
team gets an increase in revenues which offsets the mandatory decline under FFP, leading to a net
increase in wages. 31
Table 9 gives an overview of the financial variables in the counterfactual equilibria using all four
estimation approaches for the CSF. As a reference point the table includes the level of payroll and
predicted revenues in the absence of FFP (“no FFP”). Obviously, the effects of FFP are more dramatic
when the accepted deviation is smaller. Interestingly, average revenues across all regimes decrease by
less than £1.5m, well within the standard error of the simulation. This indicates that revenues are for a
large part transferred among clubs in the EPL. The average payroll in the league declines between £10m
and £16m, or 14% to 23% of its initial level. This in turn means that on average teams lower their wage-
31
E.g. Fulham under the €10m regime.
26
to-turnover ratio (wtto) by about 8% in the most liberal regime, but up to 16% when the long-term
maximum acceptable deviation is applied.
These results suggest that FFP may serve as a powerful tool for teams to coordinate on keeping
wage costs down. Indeed, we estimate the total surplus transferred from players to owners to be
between £160m to £390m, which is around 15% of total turnover in the league. Given that we have
assumed owners do not pocket any of the additional revenues their teams generate in the new regime,
these numbers should be viewed as a lower bound to the likely decrease in payrolls. A second important
remark is that we have assumed league-wide factors to be taken up by our estimates of season-division
fixed effects. If FFP would lead to an emigration of talented players from the EPL to other European
leagues, the league-wide revenue sources, such as the TV contract, might be affected. As FFP is
introduced at the European level however, it is hard to see where these players would emigrate to. If
anything one would expect FFP to hit wages equally hard in the EPL’s closest competitor leagues, such as
the Spanish La Liga.
<insert table 10 around here>
Since the goodness-of-fit measures favored the three period firm effects approach, table 10
reports the counterfactual end-of-season table using these estimates. To obtain maximum robustness
for our results, we also calculated the counterfactual points table using the other approaches for
estimating the CSF and report the results in the appendix. Table 10 shows that the traditional
powerhouses of English soccer would not be severely affected by FFP. Manchester United, Arsenal and
Liverpool consolidate their strong position in predicted points totals. These teams combine a large
revenue generating capacity with a high CSF productivity, which means that they can easily maintain
their advantage when teams have to compete within their budgets. Given the results from table 8, it is
27
noteworthy that especially Manchester United and Liverpool obtain these results setting a significantly
lower payroll.
A couple of teams would see a significant decline in their on-field performance. Most notably
Manchester City and West Ham stand to lose more than twice the bootstrapped standard error. 32 This is
again good news for the incumbent top teams, as it indicates that building a top team by spending
heavily on players in a club, which cannot (yet) produce the revenues to support this spending (which
has been the strategy of the Manchester City owners over the past couple of seasons), would become
virtually impossible.33 While Chelsea under the ownership of Roman Abramovitch since 2003, followed a
similar strategy to Manchester City over recent years, it has had longer to establish itself as a pre-
eminent club and thus does not appear to face the same difficulty in sustaining its position under FFP.
The most significant on-field gains go to teams near the bottom of the table, which so far have been able
to compete within their means, for example Wolverhampton.
7 Conclusion
In this paper we have studied the impact a specific form of financial regulation on the intensity of
competition in an industry. The effect of the regulation is to harden the budget constraint for a subset of
firms in the industry. We show that the impact of this regulation is substantial even for those firms which
are not directly affected by the regulation. Given that firms in this industry are engaged in a form of rent-
seeking contest, the regulation is expected to impact almost entirely on costs, which primarily take the
form of wages.
32
Note that the standard error for West Ham is larger than the average in the league, because for the lower part of its productivity draws the wage bill would actually have to be driven down to 0 if West Ham wants to comply with FFP. 33
Using alternative estimation procedures (see appendix) we even find that if the Financial Fair Play regime is sufficiently strict, West Ham would not be able to sustain a positive payroll. We interpret this as evidence that the revenue generating capacity and productivity of the club are too low to save the team from relegation under Financial Fair Play.
28
In particular, we find that had the Financial Fair Play regulations applied fully in the English
Premier League in the 2009/10 season, wage to turnover ratios would have fallen by as much as 15%,
which is in line with the theoretical predictions of Dietl et al (2009). As such, the FFP break-even rule will
in many ways resemble a North American salary cap, although the latter applies the same spending cap
to all teams. In other words, our paper shows that in this context a vertical restraint may restrict
competition in exactly the same way as a horizontal agreement between competing firms. Salary caps
have been justified in US courts under the theory that they promote competitive balance among the
teams. On top of this, they are agreed upon in a system of collective bargaining with unions representing
the players, and such agreements are exempt from antitrust. The break-even rule under FFP has not
been negotiated as part of a collective bargaining agreement with unions, and furthermore such
agreements are not exempt from competition law in the EU. Therefore, analyzing the impact of FFP on
competition in national leagues is important to assess whether it complies with EU competition law.
The rationale advanced by UEFA for its regulation is not the promotion of competitive balance, but
“discipline and rationality” in club finances. Considered as a vertical restraint, this might be deemed to
have pro-competitive properties if the rules help to preserve the integrity of the competition and the
financial stability of the clubs. On the other hand, our results demonstrate that the break-even rule could
be construed as a means to raising profitability and therefore an anti-competitive vertical restraint under
EU competition law.
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32
9 Tables and Figures
Figure 1: Average revenues, wage bills, profits and wage to turnover ratios in English soccer
33
Table 1: Summary statistics CSF estimation
Variable Obs Mean Std. Dev. Min Max
Primary data res 20324 1.192 0.830 0 2
home win 20324 0.458 0.498 0 1
home draw 20324 0.275 0.446 0 1
wage 20324 16.00 22.06 0.92 177.78
Season - Division year 20324 2001.4 4.858 1994 2010
division 1 20324 0.307 0.461 0 1
division 2 20324 0.407 0.491 0 1
division 3 20324 0.286 0.452 0 1
Polynomial manager tenure 20324 107.969 144.107 1 1092
tangible fixed assets 20283 26.40 50.40 0.0034 508.00
Table 2: Summary statistics revenue estimation
Variable Obs Mean Std. Dev. Min Max
revenues 1010 26.600 39.500 1.045 286
tangible fixed assets 1008 27.900 52.700 0.003 508
points 1010 60.140 15.468 11 106
relative points 1010 0.460 0.114 0.096 0.833
promoted 1010 0.132 0.338 0 1
relegated 1010 0.092 0.289 0 1
not ultimate parent 1010 0.103 0.304 0 1
year 1010 2001.732 4.900 1994 2010
division 1 1010 0.330 0.470 0 1
division 2 1010 0.368 0.483 0 1
division 3 1010 0.302 0.459 0 1
34
Table 3: Estimation Results Contest Success Function
VARIABLES no controls FE 3 period FE 4 period FE Polynomial
β1 1.4599*** 1.2064*** 0.9559*** 1.0248*** 1.3276***
(0.057) (0.105) (0.140) (0.147) (0.070)
β2 0.6133*** 0.6946*** 0.7070*** 0.7218*** 0.6659***
(0.040) (0.061) (0.085) (0.097) (0.043)
β3 0.8271*** 0.9367*** 0.9090*** 1.0433*** 0.8686***
(0.056) (0.082) (0.118) (0.140) (0.059)
αh 1.7773*** 1.7891*** 1.8090*** 1.8150*** 1.7801***
(0.032) (0.032) (0.033) (0.033) (0.032)
δ0 0.1520*** 0.1589*** 0.1832*** 0.1811*** 0.1646***
(0.021) (0.020) (0.018) (0.018) (0.020)
Average δdt 0.2947 0.2976 0.3056 0.3065 0.2975
Std. dev. δdt 0.0250 0.0253 0.0251 0.0247 0.0248
firm effects no yes yes yes no
log likelihood -20964.94 -20839.35 -20602.28 -20531.45 -20811.67
Observations 20 324 20 324 20 324 20 324 20 242 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
Table 4: Correlation between productivity measures and payroll
Correlation coefficient FE 3 period FE 4 period FE Polynomial
FE 1 3 period FE 0.736 1
4 period FE 0.692 0.881 1 Polynomial 0.685 0.569 0.609 1
Payroll All tiers 0.169 0.273 0.214 0.174
1st tier 0.339 0.517 0.444 0.312
2nd tier -0.154 -0.093 -0.079 -0.156
3rd tier -0.140 -0.077 -0.160 -0.155
35
Table 5: Summary statistics for productivity estimates
Variable Observations Mean Std. Dev. min/max
FE 1st tier 334 1 0.283 2.742
2nd tier 383 1 0.166 1.871
3rd tier 317 1 0.206 2.141
3 period FE 1st tier 334 1 0.498 5.758
2nd tier 383 1 0.294 3.191
3rd tier 317 1 0.357 4.007
4 period FE 1st tier 334 1 0.501 6.015
2nd tier 383 1 0.353 3.915
3rd tier 317 1 0.403 4.558
Polynomial 1st tier 334 1 0.208 2.023
2nd tier 382 1 0.108 1.501
3rd tier 316 1 0.101 1.480
Table 6: Estimation Results Revenue Function
VARIABLES OLS RE FE
tang fixed assets 0.118*** 0.0965*** 0.0721***
(0.00899) (0.00966) (0.00974)
points 0.880*** 0.490*** 0.376***
(0.0461) (0.0375) (0.0360)
promoted -0.0852** -0.0120 0.0216
(0.0334) (0.0245) (0.0231)
relegated 0.290*** 0.243*** 0.219***
(0.0399) (0.0291) (0.0272)
not ultimate parent 0.216*** 0.187*** 0.168***
(0.0454) (0.0495) (0.0491)
Constant 14.16*** 14.60*** 14.95***
(0.186) (0.167) (0.172)
season - division FE yes yes yes
Observations 1008 1008 1008
Overall R-squared 0.918 0.906 0.889
Hausman test value 225.70 chi-sq. 0.000 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
36
Table 7: Summary statistics and measures of fit for end-of season points
Real null no controls FE 3 period FE 4 period FE Polynomial
Average 53.47 51.81 52.24 52.45 52.25 52.18 52.46
St. Dev. 17.70 0 14.60 14.59 17.23 17.13 15.69
RMSE - 17.31 8.10 7.79 5.87 6.02 7.52
MAE - 14.81 7.10 6.09 4.83 4.88 5.93
Table 8: Wage differences in equilibrium with 3 period FE
team Original final € 5m € 10m € 15m
Chelsea 172.6 -61.6* (0.8) -59.0* (0.8) -55.0* (0.9) -50.8* (0.9)
Manchester City 133.3 -88.8* (3.0) -85.9* (3.0) -81.1* (2.9) -76.3* (2.5)
Manchester United 131.7 -14.5* (1.7) -12.0* (0.7) -8.0* (0.5) -3.8* (0.5)
Liverpool 121.1 -24.4* (0.2) -21.8* (0.1) -17.8* (0.1) -13.5* (0.1)
Arsenal 110.7 3.8 (0.9) 3.2 (0.8) 2.5 (0.6) 2.0 (0.5)
Aston Villa 80.0 -32.6* (0.7) -29.6* (0.8) -25.1* (0.7) -20.4* (0.6)
Tottenham 67.1 4.4 (1.3) 3.6 (1.0) 2.7 (0.7) 2.1 (0.6)
Everton 54.3 2.3 (0.7) 1.9 (0.5) 1.4 (0.4) 1.1 (0.3)
Sunderland 53.7 -23.0* (1.1) -19.4* (1.0) -14.0* (0.7) -8.6* (0.3)
West Ham 53.6 -32.4* (7.6) -28.1* (4.8) -22.0* (1.6) -16.3* (1.0)
Fulham 49.3 -6.5* (0.5) -3.6* (0.3) 0.9* (0.3) 1.0 (0.2)
Blackburn 47.4 2.3 (0.7) 1.9 (0.5) 1.4 (0.3) 1.1 (0.3)
Bolton 46.4 -19.5* (0.7) -16.1* (0.6) -11.0* (0.3) -6.0* (0.1)
Stoke 44.8 0.0* (0.5) 1.3 (0.4) 1.0 (0.2) 0.7 (0.2)
Wigan 39.4 -5.3* (0.2) -2.4* (0.2) 0.7 (0.2) 0.5 (0.1)
Hull 38.3 -2.7* (0.5) 0.2* (0.4) 1.0 (0.3) 0.7 (0.2)
Birmingham 36.7 -2.3* (0.8) 0.8* (0.7) 1.7 (0.5) 1.3 (0.3)
Wolverhampton 29.8 4.7 (2.0) 3.8 (1.5) 2.7 (1.0) 2.0 (0.7)
Burnley 22.4 2.1 (0.9) 1.6 (0.6) 1.1 (0.4) 0.8 (0.2) * indicates that club is restricted by FFP, bootstrapped standard error in parentheses.
37
Table 9: Simulation Results
Variable no FFP final € 5m € 10m € 15m
rev FE 104.7 (5.6) 103.5 (5.4) 104.2 (5.4) 104.3 (5.5) 104.4 (5.5)
3 period FE 105.1 (5.5) 104.7 (5.5) 104.7 (5.5) 104.8 (5.5) 104.8 (5.5)
4 period FE 105.1 (5.6) 104.6 (5.4) 104.7 (5.5) 104.7 (5.5) 104.8 (5.5)
Polynomial 105.0 (5.6) 103.6 (5.5) 103.6 (5.4) 104.5 (5.4) 104.6 (5.6)
wage FE 70.1 54.5 (0.2) 56.3 (0.2) 58.6 (0.1) 60.4 (0.1)
3 period FE 70.1 54.7 (0.1) 56.5 (0.1) 58.7 (0.1) 60.5 (0.1)
4 period FE 70.1 54.6 (0.2) 56.4 (0.2) 58.7 (0.1) 60.5 (0.1)
Polynomial 70.1 54.5 (0.6) 56.1 (0.2) 58.5 (0.2) 60.4 (0.1)
wtto FE 73.2% (3.7) 57.6% (3.1) 60.8% (3.3) 63.6% (3.3) 65.5% (3.4)
3 period FE 73.9% (3.8) 59.0% (3.2) 61.6% (3.3) 64.4% (3.3) 66.1% (3.4)
4 period FE 74.0% (3.9) 58.9% (3.2) 61.6% (3.3) 64.4% (3.4) 66.1% (3.5)
Polynomial 73.5% (3.8) 57.8% (2.9) 60.1% (3.2) 63.9% (3.5) 65.7% (3.4)
Bootstrap standard errors in parentheses, obtained from 200 simulations using independent parameter draws.
38
Table 10: Points Table using 3 period fixed effects
Team Real No FFP Final € 5m € 10m € 15m
Chelsea 86 86.6 (3.9) 83.7 (4.3) 83.6 (4.3) 83.5 (4.4) 83.6 (4.4)
Manchester Utd. 85 83.7 (4.3) 85.0 (4.1) 84.8 (4.2) 84.7 (4.2) 84.8 (4.2)
Arsenal 75 72.3 (4.3) 76.3 (3.9) 75.6 (4.0) 74.9 (4.1) 74.3 (4.2)
Tottenham 70 58.7 (3.6) 63.7 (3.6) 62.8 (3.6) 61.7 (3.6) 61.0 (3.6)
Manchester City 67 60.6 (4.0) 45.3 (4.1) 45.6 (4.2) 46.4 (4.2) 47.4 (4.1)
Aston Villa 64 58.6 (3.4) 53.3 (3.6) 53.6 (3.6) 54.3 (3.6) 55.2 (3.5)
Liverpool 63 74.3 (4.1) 74.2 (4.0) 74.0 (4.1) 73.9 (4.1) 74.1 (4.1)
Everton 61 59.5 (3.8) 64.1 (3.8) 63.2 (3.8) 62.3 (3.8) 61.7 (3.8)
Birmingham 50 39.5 (3.6) 42.1 (3.9) 42.8 (3.9) 42.3 (3.8) 41.6 (3.8)
Blackburn 50 49.2 (3.4) 53.9 (3.5) 53.0 (3.5) 52.0 (3.5) 51.3 (3.5)
Stoke 47 44.1 (3.6) 48.0 (3.9) 47.7 (3.8) 46.7 (3.8) 46.1 (3.7)
Fulham 46 43.5 (3.4) 44.9 (3.4) 45.2 (3.4) 46.0 (3.5) 45.5 (3.5)
Sunderland 44 38.2 (3.3) 33.0 (3.1) 33.9 (3.2) 35.4 (3.2) 36.9 (3.2)
Bolton 39 46.0 (3.7) 40.6 (3.6) 41.8 (3.7) 43.5 (3.7) 45.3 (3.7)
Wolverhampton 38 33.8 (3.1) 39.7 (3.8) 38.5 (3.5) 37.2 (3.3) 36.3 (3.3)
Wigan 36 42.2 (3.9) 43.6 (4.0) 44.2 (3.9) 44.7 (4.0) 44.1 (4.0)
West Ham 35 41.5 (3.0) 30.5 (8.0) 32.5 (5.6) 35.0 (3.2) 37.1 (3.1)
Burnley 30 27.8 (2.9) 32.3 (3.3) 31.3 (3.2) 30.2 (3.0) 29.6 (3.0)
Hull 30 32.7 (3.5) 35.1 (3.8) 35.5 (3.8) 35.1 (3.7) 34.4 (3.7)
Portsmouth 19 49.0 (3.8) 52.9 (3.8) 52.1 (3.8) 51.3 (3.9) 50.7 (3.9) Bootstrap standard errors in parentheses, obtained from 200 simulations using independent parameter draws.
39
10 Appendix
10.1 Full table Fixed Effects
Team Real no FFP final € 5m € 10m € 15m
Chelsea 86 77.3 (2.0) 72.9 (2.0) 72.3 (2.1) 71.9 (2.1) 72.0 (2.1)
Manchester Utd. 85 81.0 (2.2) 83.3 (2.1) 82.9 (2.1) 82.7 (2.2) 82.7 (2.2)
Arsenal 75 74.6 (2.1) 80.1 (2.0) 79.1 (2.0) 78.1 (2.0) 77.3 (2.0)
Tottenham 70 50.9 (1.7) 59.6 (2.1) 57.4 (2.1) 55.6 (2.0) 54.4 (1.8)
Manchester City 67 64.1 (2.5) 43.6 (3.7) 42.1 (2.5) 43.4 (2.4) 45.1 (2.3)
Aston Villa 64 60.3 (2.0) 54.1 (2.0) 53.4 (2.0) 54.3 (2.0) 55.5 (2.0)
Liverpool 63 69.5 (2.1) 70.0 (2.1) 69.3 (2.2) 69.1 (2.2) 69.2 (2.2)
Everton 61 48.0 (2.0) 55.9 (2.2) 53.7 (2.2) 52.1 (2.2) 51.0 (2.1)
Birmingham 50 42.0 (1.7) 48.0 (2.0) 47.4 (2.1) 46.5 (1.9) 45.4 (1.8)
Blackburn 50 46.5 (1.7) 54.5 (1.8) 52.2 (1.8) 50.5 (1.7) 49.5 (1.7)
Stoke 47 45.9 (2.0) 52.6 (2.2) 51.2 (2.3) 49.6 (2.2) 48.7 (2.1)
Fulham 46 45.6 (2.1) 49.2 (2.2) 48.4 (2.3) 49.3 (2.2) 48.5 (2.2)
Sunderland 44 47.7 (1.9) 41.8 (4.3) 40.8 (2.1) 43.3 (2.0) 45.8 (2.0)
Bolton 39 49.6 (1.9) 43.8 (1.9) 43.6 (2.1) 46.2 (2.0) 48.7 (1.9)
Wolverhampton 38 35.8 (1.8) 47.6 (2.4) 44.0 (2.6) 41.6 (2.1) 40.1 (1.8)
Wigan 36 45.4 (2.0) 48.8 (2.1) 48.4 (2.2) 49.0 (2.1) 48.0 (2.1)
West Ham 35 45.8 (1.9) 6.4 (11.9) 28.4 (12.5) 35.0 (7.2) 38.9 (2.4)
Burnley 30 29.5 (1.6) 39.0 (2.1) 35.4 (2.2) 33.4 (1.8) 32.3 (1.6)
Hull 30 37.1 (2.4) 42.6 (2.5) 41.7 (2.7) 40.7 (2.5) 39.7 (2.5)
Portsmouth 19 45.9 (1.9) 52.1 (2.2) 50.2 (2.2) 49.0 (2.1) 48.2 (2.0) Bootstrap standard errors in parentheses, obtained from 200 simulations using independent parameter draws.
10.2 Full table 4 period Fixed Effect
Team Real no FFP final €5m € 10m € 15m
Chelsea 86 84.2 (6.6) 80.9 (6.6) 80.7 (6.9) 80.6 (7.0) 80.7 (7.0)
Manchester Utd. 85 83.9 (5.9) 85.2 (5.5) 85.1 (5.8) 85.0 (5.9) 85.1 (5.9)
Arsenal 75 71.2 (3.8) 75.6 (3.5) 74.8 (3.6) 74.0 (3.6) 73.4 (3.7)
Tottenham 70 58.8 (3.8) 64.3 (3.9) 63.3 (3.8) 62.2 (3.8) 61.4 (3.8)
Manchester City 67 60.9 (4.6) 44.1 (5.7) 44.4 (4.5) 45.3 (4.4) 46.4 (4.3)
Aston Villa 64 59.4 (3.4) 53.7 (3.4) 54.0 (3.5) 54.8 (3.5) 55.7 (3.5)
Liverpool 63 76.5 (5.5) 76.4 (5.2) 76.2 (5.5) 76.2 (5.5) 76.4 (5.5)
Everton 61 58.7 (3.6) 63.7 (3.7) 62.8 (3.7) 61.7 (3.7) 61.0 (3.7)
Birmingham 50 39.6 (3.7) 42.7 (4.0) 43.3 (4.0) 42.8 (3.9) 42.0 (3.8)
Blackburn 50 49.8 (3.6) 55.1 (3.7) 54.0 (3.7) 52.9 (3.6) 52.2 (3.6)
40
Stoke 47 44.5 (3.6) 48.8 (4.0) 48.5 (4.0) 47.4 (3.9) 46.7 (3.8)
Fulham 46 44.0 (3.2) 45.7 (3.4) 46.0 (3.4) 46.8 (3.4) 46.3 (3.3)
Sunderland 44 37.0 (3.8) 31.3 (3.7) 32.3 (3.7) 33.9 (3.8) 35.5 (3.8)
Bolton 39 44.8 (3.6) 39.0 (3.4) 40.2 (3.6) 42.2 (3.6) 44.0 (3.6)
Wolverhampton 38 34.9 (3.3) 41.7 (3.9) 40.3 (3.7) 38.7 (3.5) 37.7 (3.4)
Wigan 36 40.6 (3.8) 42.1 (3.8) 42.7 (3.9) 43.2 (4.0) 42.5 (3.9)
West Ham 35 42.1 (3.8) 29.3 (11.3) 31.9 (7.9) 34.8 (4.6) 37.2 (3.8)
Burnley 30 27.5 (3.0) 32.6 (3.5) 31.4 (3.3) 30.2 (3.1) 29.5 (3.1)
Hull 30 33.1 (3.3) 35.8 (3.9) 36.3 (3.7) 35.7 (3.6) 35.0 (3.5)
Portsmouth 19 50.3 (4.3) 54.6 (4.5) 53.7 (4.5) 52.8 (4.4) 52.2 (4.4) Bootstrap standard errors in parentheses, obtained from 200 simulations using independent parameter draws.
10.3 Full table productivity polynomial
Team Real no FFP final 5m € 10m € 15m €
Chelsea 86 74.2 (2.4) 68.9 (2.4) 68.5 (2.4) 67.8 (2.4) 67.9 (2.4)
Manchester Utd. 85 81.3 (4.5) 83.8 (4.1) 83.6 (4.3) 83.3 (4.3) 83.3 (4.4)
Arsenal 75 77.6 (4.3) 83.1 (3.9) 82.4 (4.0) 81.3 (4.1) 80.6 (4.2)
Tottenham 70 54.2 (1.1) 63.5 (1.4) 62.2 (1.4) 59.6 (1.4) 58.3 (1.2)
Manchester City 67 68.6 (2.1) 45.3 (5.9) 46.3 (4.7) 45.8 (2.7) 47.8 (2.6)
Aston Villa 64 62.1 (1.1) 55.2 (1.6) 55.8 (1.3) 55.6 (1.2) 57.0 (1.2)
Liverpool 63 72.9 (1.6) 73.5 (1.6) 73.2 (1.6) 72.7 (1.6) 72.9 (1.6)
Everton 61 51.4 (1.4) 59.9 (1.7) 58.7 (1.8) 56.1 (1.7) 54.9 (1.6)
Birmingham 50 39.4 (0.9) 46.2 (1.3) 47.2 (1.6) 44.4 (1.5) 43.0 (1.0)
Blackburn 50 44.1 (0.7) 53.1 (1.2) 51.9 (1.3) 48.7 (1.2) 47.5 (0.8)
Stoke 47 45.1 (1.7) 52.5 (1.8) 52.2 (1.9) 49.3 (1.9) 48.2 (1.7)
Fulham 46 46.6 (1.0) 50.5 (1.2) 51.1 (1.3) 50.8 (1.3) 49.8 (1.1)
Sunderland 44 45.4 (1.2) 38.8 (5.9) 40.8 (3.0) 40.3 (1.6) 43.2 (1.3)
Bolton 39 43.0 (0.6) 37.3 (4.1) 39.2 (1.4) 39.1 (1.1) 41.8 (0.6)
Wolverhampton 38 35.6 (1.2) 49.0 (1.9) 47.4 (2.3) 42.5 (2.2) 40.7 (1.5)
Wigan 36 39.4 (1.0) 43.4 (1.2) 44.3 (1.4) 43.2 (1.4) 42.1 (1.1)
West Ham 35 48.5 (0.8) 6.1 (11.9) 6.0 (13.3) 35.5 (10.6) 40.4 (1.5)
Burnley 30 27.6 (1.0) 38.2 (1.3) 36.8 (1.9) 31.9 (1.7) 30.6 (1.0)
Hull 30 39.7 (1.2) 45.5 (1.4) 46.4 (1.6) 43.9 (1.5) 42.7 (1.3)
Portsmouth 19 45.6 (1.0) 52.4 (1.2) 51.4 (1.3) 49.0 (1.3) 48.1 (1.1) Bootstrap standard errors in parentheses, obtained from 200 simulations using independent parameter draws.
